\lim_{ x \to \infty }\frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x}+\sqrt{x+2}-\sqrt{4x+12}}\lim_{ x \to \infty }\frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x}+\sqrt{x+2}-\sqrt{4x+12}}

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